{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $$MonoForest\\ Framework\\ Tutorial$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/catboost/tutorials/blob/master/model_analysis/monoforest_tutorial.ipynb)\n",
    "\n",
    "##### $MonoForest$ is a framework to transform ensemble of decision trees from traditional graph model to polynomial form.\n",
    "##### Polynomial is a sum of monomials.\n",
    "##### Each monomial is defined by:\n",
    "* value (how much prediction value changes)\n",
    "* set of conditions (a.k.a splits)\n",
    "* weight (how much points from learning dataset satisfy conditions of this monomial).\n",
    "##### Polinomial form allows to do model-wide analysis instead of tree-wide.\n",
    "##### In this tutorial we will see how analysis of model can be performed with help of MonoForest framework.\n",
    "##### Framework is based on the paper \"MonoForest framework for tree ensemble analysis\" by Igor Kuralenok, Vasily Ershov and Igor Labutin [<a>https://nips.cc/Conferences/2019/Schedule?showEvent=14311</a>]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-13T14:48:36.723179Z",
     "start_time": "2019-11-13T14:48:36.155242Z"
    }
   },
   "outputs": [],
   "source": [
    "# Import necessary libraries\n",
    "from catboost import CatBoostClassifier, CatBoostRegressor, monoforest\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example with Boston dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the first example let's take 'Boston' dataset from sklearn. This dataset contains features of houses and the target is price of houses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-13T14:48:38.660986Z",
     "start_time": "2019-11-13T14:48:38.332496Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of features:  (506, 13)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import load_boston\n",
    "\n",
    "boston = load_boston()\n",
    "print(\"Shape of features: \", boston.data.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's train small model to see polynomial representation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-14T07:31:29.695268Z",
     "start_time": "2019-11-14T07:31:29.629477Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0:\tlearn: 9.0093958\ttotal: 7.64ms\tremaining: 30.6ms\n",
      "1:\tlearn: 8.8366476\ttotal: 11ms\tremaining: 16.5ms\n",
      "2:\tlearn: 8.6816967\ttotal: 16.2ms\tremaining: 10.8ms\n",
      "3:\tlearn: 8.5510603\ttotal: 21.2ms\tremaining: 5.3ms\n",
      "4:\tlearn: 8.4259116\ttotal: 25.8ms\tremaining: 0us\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<catboost.core.CatBoostRegressor at 0x7f9a95515190>"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = CatBoostRegressor(iterations=5, max_depth=3)\n",
    "model.fit(boston.data, boston.target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-13T14:48:52.968071Z",
     "start_time": "2019-11-13T14:48:52.962231Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-0.3360926600712766) * [F9 > 567.5][F12 > 10.25] <weight=125.0>,\n",
       " (0.23854733322046123) * [F5 > 7.121000289916992] <weight=54.0>,\n",
       " (-0.17118946623380893) * [F12 > 10.25] <weight=279.0>,\n",
       " (-0.5535056303820198) * [F5 > 7.014999866485596][F9 > 567.5] <weight=5.0>,\n",
       " (-0.5951303926761635) * [F0 > 7.036504745483398][F5 > 6.753999710083008] <weight=8.0>,\n",
       " (0.36221767157908635) * [F5 > 6.753999710083008] <weight=101.0>,\n",
       " (-0.09869084562936245) * [F5 > 6.30150032043457][F9 > 387.5] <weight=74.0>,\n",
       " (-0.3630028988160471) * [F0 > 7.036504745483398][F12 > 11.235000610351562] <weight=81.0>,\n",
       " (0.20142226122176154) * [F9 > 567.5] <weight=137.0>,\n",
       " (-0.2638978511901868) * [F5 > 7.014999866485596][F12 > 10.25] <weight=3.0>,\n",
       " (0.3342530345325465) * [F7 > 2.1052498817443848][F12 > 9.675000190734863] <weight=186.0>,\n",
       " (0.026750982764025377) * [F5 > 7.121000289916992][F6 > 64.89999389648438] <weight=27.0>,\n",
       " (-0.15088079141862987) * [F12 > 11.235000610351562] <weight=257.0>,\n",
       " (0.08886858200450351) * [F5 > 6.8454999923706055][F6 > 64.89999389648438] <weight=40.0>,\n",
       " (0.05306861885154894) * [F5 > 6.947000026702881][F9 > 387.5] <weight=16.0>,\n",
       " (-0.06491458687139842) * [F7 > 2.1052498817443848][F12 > 4.550000190734863] <weight=339.0>,\n",
       " (-0.14719424771631195) * [F6 > 64.89999389648438] <weight=308.0>,\n",
       " (-0.25312409754504045) * [F12 > 4.550000190734863] <weight=462.0>,\n",
       " (-0.14314432541017225) * [F5 > 6.753999710083008][F12 > 11.235000610351562] <weight=12.0>,\n",
       " (0.4270016792758895) * [F5 > 7.014999866485596] <weight=62.0>,\n",
       " (0.5510783989340879) * [F5 > 7.014999866485596][F9 > 567.5][F12 > 10.25] <weight=2.0>,\n",
       " (0.3324986578872847) * [F5 > 6.947000026702881] <weight=75.0>,\n",
       " (-0.11157911816935517) * [F7 > 2.1052498817443848] <weight=377.0>,\n",
       " (0.19936781885819355) * [F0 > 7.036504745483398] <weight=84.0>,\n",
       " (-0.09151221523922708) * [F9 > 387.5] <weight=220.0>,\n",
       " (23.13211801836055) <weight=506.0>,\n",
       " (0.17947742206269401) * [F5 > 6.8454999923706055] <weight=86.0>,\n",
       " (-0.5241129673290377) * [F12 > 9.675000190734863] <weight=297.0>,\n",
       " (0.4805471747489617) * [F0 > 7.036504745483398][F5 > 6.753999710083008][F12 > 11.235000610351562] <weight=8.0>,\n",
       " (0.1412904452021207) * [F5 > 6.30150032043457] <weight=224.0>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "monoforest.to_polynom(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that polynomial contains conditions primarly with features 2, 5, 7 and 12. Possibly these features contains the most important information. Now let's fit a bigger model and explore dependence of target value on each feature and average influence of each feature on predicted value (features strength)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-13T14:48:59.348208Z",
     "start_time": "2019-11-13T14:48:55.947510Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0:\tlearn: 9.0076390\ttotal: 6.99ms\tremaining: 342ms\n",
      "10:\tlearn: 7.5884310\ttotal: 65.1ms\tremaining: 231ms\n",
      "20:\tlearn: 6.4249574\ttotal: 121ms\tremaining: 167ms\n",
      "30:\tlearn: 5.5547127\ttotal: 180ms\tremaining: 110ms\n",
      "40:\tlearn: 4.9241776\ttotal: 238ms\tremaining: 52.3ms\n",
      "49:\tlearn: 4.4267805\ttotal: 296ms\tremaining: 0us\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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rSaEBKmkYWXjOi4iFJe1nADOAUyIiynR9AngiIrr2WG8kC9TXiIi5EdESES0NDQ1Vrd/MbHuKvAovsnOYKyPi8pL2acAFwHER8WK5vhHxe2CtpP1S09FAR1G1mpnlMbTAdR8JnAY8KKk9tV0MXAG8DliSZSx3RcTHJI0DromI6WnZjwPzJO0KPAp8qMBazcx6rbAAjYg7AJX5alEPy68Hppd8bgdaiqnOzGznFbkHalYXOjo3ceLVdwLZIMuzWptqXJHVix2eA5W0r6SfSnoofT5Q0qeLL82seDMnN9I8dhSQBalHp7feqOQi0r+TPS30MkBEPACcVGRRZn1lVmsT88+eyvyzp24NUrNKVRKgu0XE3d3atpRd0sxsEKkkQJ+W9FdAAEg6AegstCozszpQyUWkc4C5wP6S1gGrgVMLrcrMrA7sMEAj4lHgXelZ9F3SwCBmZoPeDgNU0me7fQYgIi4tqCYzs7pQySH8CyXvh5M9w+6xOc1s0KvkEP5fSj9L+hpwe2EVmZnViTyDiexGmUGQzcwGm0rOgT5IuoUJGAI0AD7/aWaDXiXnQGeUvN8CPFkyJYfZgOLn4q03egxQSWPS2+63LY2SRERsLK4ss743c3Lj1vcdndnkCQ5Q257t7YHeS3boXm5IugDeUkhFZjUyq7Vpa2B27YWabU+PARoRk/qyEDOzelPReKCS9gT2IbsPFICI+GVRRZmZ1YNKrsJ/BJhNdutSOzAFuBM4qtjSzMz6t0ruA50NHAY8HhHvJJvf/dlCqzIzqwOVBOgfI+KPAJJeFxGrgP120MfMbMCr5BzoE5JGAz8km0nzGeDxYssyM+v/KnkW/v3p7eckLQX2AP6z0KrMzOpAJReRrgC+HxG/johf9EFNZmZ1oZJzoPcCn5b0O0lfk+S52s3MqCBAI+I7ETGd7Er8w8BXJf2m8MrMzPq53gxn91Zgf2BvYFUx5Zj1H22rN3JD25pal2H92A4DVNI/pz3OS4EHgZaIOLbwysxqqGtgkZvb19W4EuvPKrmN6XfA1Ih4uuhizPqLWa1NDk/boUrOgV6dJzwlTZC0VFKHpBWSZqf2yyStkvSApJvSPaY9rWOIpPsk3drb3zczK1qeKT0qtQU4PyKayZ6fP0dSM7AEOCAiDgQeAS7azjpm4wnszKyfKixAI6IzIpan95vJgrAxIhaXjGh/Fz3MryRpPPA+4JqiajQz2xmVjEhfVm9GpJc0kWwQkrZuX50JzO+h2zeAC4DdK/0dM7O+VPiI9JJGAguA8yJiU0n7JWSH+fPK9JkBPBUR90p6xw7WfxZwFkBTk6dfMLO+U+iI9JKGkYXnvIhYWNJ+BtlkdUdHRJTpeiRwnKTpZIM4j5J0fUScWqbOucBcgJaWlnLrMjMrRCX3gUrSqZI+kz43STq8kn7AtcDKiLi8pH0a2aH5cRHxYrm+EXFRRIyPiInAScDPyoWnmVktVXIR6V+BqcCs9Hkz8K0K+h0JnAYcJak9vaYDV5Kd11yS2q4CkDRO0qJeb4GZWY1UciN9a0QcIuk+gIh4RtKuO+oUEXdQ/vxp2ZCMiPXA9DLtPwd+XkGdZmZ9qpI90JclDSG7cISkBuDVQqsyM6sDlQToFcBNwBslfQm4A/hyoVWZmdWBSkaknyfpXuBoskPy4yPCTweZ2aDX4x6opDFdL+Ap4HvADcCTO7rJ3myg6OjcxIlX3+lh7aysSm+kbwKeSe9HA2uAnb5P1Kw/6xrSrqMze/5jVqsf1LBt9bgHGhGTIuItwE+AYyNir4h4A9kN8Iv7qkCzWpnV2sT8s6fSPHZUrUuxfqqSi0hTImLrrUcRcRtwRHElmZnVh0ruA10v6dPA9enzKcD64koyM6sPleyBngw0kN3KdBPwxtRmZjaoVXIb00ZgtqTds4/xfPFlmZn1f5UMJvI/02OcDwErJN0r6YDiSzMz698qOYS/Gvg/EbF3ROwNnE8aPs7MbDCrJEBHRMTSrg9pcI8RhVVkZlYnKrkK/2gaC/S76fOpwKPFlWRmVh8q2QM9k+wq/ML0akhtZmaDWiVX4Z8Bzu2DWszM6soOA1RSC3AxMLF0+TSvu5nZoFXJOdB5wD8BD+KBlM3MtqokQDdExC2FV2JmVmcqCdA5kq4Bfgr8qauxdJpiM7PBqJIA/RCwPzCMvxzCB9kVeTOzQauSAD0sIvYrvBIzszpTyX2gv5bUXHglZmZ1ppI90ClAu6TVZOdARTYqk29jMrNBrZIAnVZ4FWZmdaiSJ5Ee74tCzMzqTSXnQM3MrAwHqJlZToUFqKQJkpZK6pC0QtLs1H6ZpFWSHpB0k6TRlfY1M+tPitwD3QKcHxHNZFfyz0m3Qy0BDkhX8R8BLupFXzOzfqOwAI2IzohYnt5vBlYCjRGxOCK2pMXuAsZX2reoWs3M8uiTc6CSJgIHA23dvjoTuC1nXzOzmio8QCWNBBYA50XEppL2S8gO1ef1tm+3Zc6StEzSsg0bNlS3eDOz7Sg0QCUNIwvAeaWjN0k6A5gBnBIR0Zu+3UXE3IhoiYiWhoaGqtZvZrY9lTyJlIskAdcCKyPi8pL2acAFwNsj4sXe9DUz60+K3AM9EjgNOEpSe3pNB64EdgeWpLarACSNk7RoB33NzPqNwvZAI+IOsoFHultUpo2IWA9M30FfM7N+w08imZnl5AA1M8vJAWpmlpMD1MwsJweomVlODlAzs5wcoGZmOTlAzcxycoCameXkADUzy8kBamaWkwPUzCwnB6iZWU4OUDOznBygZmY5OUDNzHJygJqZ5eQANTPLyQFqZpaTA9TMLCcHqJlZTg5QM7OcHKBmZjk5QM3McnKAmpnl5AA1M8vJAWpmlpMD1Mwsp8ICVNIESUsldUhaIWl2ar9M0ipJD0i6SdLoHvpPk/SwpN9KurCoOs3M8ipyD3QLcH5ENANTgHMkNQNLgAMi4kDgEeCi7h0lDQG+BRwDNAMnp75mZv1GYQEaEZ0RsTy93wysBBojYnFEbEmL3QWML9P9cOC3EfFoRPwZ+D4ws6hazczy6JNzoJImAgcDbd2+OhO4rUyXRmBtyecnUpuZWb9ReIBKGgksAM6LiE0l7ZeQHebP28n1nyVpmaRlGzZs2LlizXrQ0bmJE6++kxva1tS6FOtHCg1QScPIwnNeRCwsaT8DmAGcEhFRpus6YELJ5/Gp7TUiYm5EtERES0NDQ9VqN+syc3IjzWNH0dG5iZvby/4xtEGqyKvwAq4FVkbE5SXt04ALgOMi4sUeut8D7CNpkqRdgZOAW4qq1Wx7ZrU2Mf/sqTSPHVXrUqyfKXIP9EjgNOAoSe3pNR24EtgdWJLargKQNE7SIoB0kekfgdvJLj79ICJWFFirmVmvDS1qxRFxB6AyXy3qYfn1wPSSz4t6WtbMrD/wk0hmZjk5QM3McnKAmpnl5AA1M8vJAWpmlpMD1MwsJweomVlODlAzs5wcoGZmOTlAzcxycoCameXkADUzy8kBamaWkwPUzCwnB6iZWU4OUDOznBygZmY5OUDNzHJygJqZ5eQANTPLyQFqZpaTA9TMLCcHqJlZTg5QM7OcHKBmZjk5QM3McnKAmpnl5AA1M8upsACVNEHSUkkdklZImp3a/y59flVSy3b6fyIt95Ck70kaXlStZpXq6NzEiVffyQ1ta2pdivUDRe6BbgHOj4hmYApwjqRm4CHgfwG/7KmjpEbgXKAlIg4AhgAnFVir2Q7NnNxI89hRdHRu4ub2dbUux/qBwgI0IjojYnl6vxlYCTRGxMqIeLiCVQwFXi9pKLAbsL6oWs0qMau1iflnT6V57Khal2L9xNC++BFJE4GDgbZKlo+IdZK+BqwBXgIWR8TiHtZ9FnAWQFNTUzXKNeuVG9rWeI+0jjSPG8WcY99WlXUVfhFJ0khgAXBeRGyqsM+ewExgEjAOGCHp1HLLRsTciGiJiJaGhoZqlW1WsZvb19HRWdEfbRtgCt0DlTSMLDznRcTCXnR9F7A6Ijak9SwEjgCur36VZjuveewo5p89tdZlWB8r8iq8gGuBlRFxeS+7rwGmSNotredosnOoZmb9RpGH8EcCpwFHSWpPr+mS3i/pCWAq8GNJtwNIGidpEUBEtAE3AsuBB1Odcwus1axX2lZv9K1MVtwhfETcAaiHr28qs/x6YHrJ5znAnGKqM8tv5uRG2lZv5Ob2dcxq9YXLwcxPIpn10qzWJlonjal1GdYPOEDNzHJygJqZ5eQANTPLyQFqllPXwCK+iX7w6pNHOc0GmpmTG7e+bx47apvPNng4QM1ymNXa5FuYzIfwZmZ5OUDNzHJygJqZ5eQANTPLyQFqZpaTA9TMLCcHqJlZTg5QM7OcHKBmZjk5QM3McnKAmpnlpIiodQ1VI2kD8HgNS9gLeLqGv9+XvK0D02DZ1t5u594R8Zp50wdUgNaapGUR0VLrOvqCt3VgGizbWq3t9CG8mVlODlAzs5wcoNU1mOau97YOTINlW6uynT4HamaWk/dAzcxycoBWiaRpkh6W9FtJF9a6nmqSdJ2kpyQ9VNI2RtISSb9J/9yzljVWg6QJkpZK6pC0QtLs1D4Qt3W4pLsl3Z+29fOpfZKktvTneL6kXWtdazVIGiLpPkm3ps9V2U4HaBVIGgJ8CzgGaAZOltRc26qq6tvAtG5tFwI/jYh9gJ+mz/VuC3B+RDQDU4Bz0n/HgbitfwKOioiDgMnANElTgK8CX4+ItwLPAB+uYY3VNBtYWfK5KtvpAK2Ow4HfRsSjEfFn4PvAzBrXVDUR8UtgY7fmmcB30vvvAMf3aVEFiIjOiFie3m8m+x+ukYG5rRERz6ePw9IrgKOAG1P7gNhWSeOB9wHXpM+iStvpAK2ORmBtyecnUttA9qaI6Ezvfw+8qZbFVJukicDBQBsDdFvTYW078BSwBPgd8GxEbEmLDJQ/x98ALgBeTZ/fQJW20wFqOy2yWzkGzO0ckkYCC4DzImJT6XcDaVsj4pWImAyMJzuK2r/GJVWdpBnAUxFxbxHr97zw1bEOmFDyeXxqG8ielDQ2IjoljSXbi6l7koaRhee8iFiYmgfktnaJiGclLQWmAqMlDU17ZwPhz/GRwHGSpgPDgVHAN6nSdnoPtDruAfZJV/Z2BU4CbqlxTUW7BTg9vT8duLmGtVRFOjd2LbAyIi4v+WogbmuDpNHp/euBd5Od810KnJAWq/ttjYiLImJ8REwk+//yZxFxClXaTt9IXyXpb7hvAEOA6yLiSzUuqWokfQ94B9kINk8Cc4AfAj8AmshGwPrfEdH9QlNdkfTXwK+AB/nL+bKLyc6DDrRtPZDs4skQsh2pH0TEpZLeQnYRdAxwH3BqRPypdpVWj6R3AJ+MiBnV2k4HqJlZTj6ENzPLyQFqZpaTA9TMLCcHqJlZTg5QM7OcHKBWE5LOlbRS0rwcfSdKmlVEXXlI+pykT9a6Dut7DlCrlX8A3p1uau6tiUCvAzSNmmVWNQ5Q63OSrgLeAtwm6ROSRqQxR+9OYzbOTMtNlPQrScvT64i0iq8AfyOpPfU/Q9KVJeu/Nd00jaTnJf2LpPuBqZIOlfQLSfdKuj09mlla2x6SHpe0S/o8QtJaScMkfVTSPWkMzQWSdiuzbT+X1JLe7yXpsfR+iKTLUv8HJJ1d5X+tVgMOUOtzEfExYD3wzoj4OnAJ2SN2hwPvBC6TNILsmfN3R8QhwInAFWkVFwK/iojJqf/2jADa0riXbcD/A06IiEOB64BtnhiLiOeAduDtqWkGcHtEvAwsjIjD0rpW0rsxJD8MPBcRhwGHAR+VNKkX/a0f8mAi1h+8h2zAh67ziMPJHptcD1wpaTLwCrBvjnW/QjY4CMB+wAHAkuyxd4YAnWX6zCcL7KVkz0//a2o/QNIXgdHASOD2XtTxHuBASV3PX+8B7AOs7sU6rJ9xgFp/IOADEfHwNo3S58ievT+I7Gjpjz3038K2R1PDS97/MSJeKfmdFRExdQf13AJ8WdIY4FDgZ6n928DxEXG/pDPIxgfYXi2ldQj4eET0JnStn/MhvPUHtwMfT6MhIeng1L4H0BkRrwKnke0xAmwGdi/p/xgwWdIukiaQjW1ZzsNAg6Sp6XeGSXpb94XSSO33kA17dmtJAO8OdHtkF3YAAAC1SURBVKYh73q6+PUYWejCX0b76drGv099kbRvOk1hdcwBav3BF8imlHhA0or0GbJD59PTBaD9gRdS+wPAK+lizieA/yI7FO4gO0+6vNyPpOlWTgC+mtbZDhxRblmyw/hT0z+7fIbsPOp/Aat66Pc1sqC8j2z0qi7XpPqWK5uc72p8BFj3PBqTmVlO3gM1M8vJAWpmlpMD1MwsJweomVlODlAzs5wcoGZmOTlAzcxycoCameX037qIUQ/diYxlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = CatBoostRegressor(iterations=50)\n",
    "model.fit(boston.data, boston.target, verbose=10)\n",
    "monoforest.plot_pdp(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-13T14:48:59.644101Z",
     "start_time": "2019-11-13T14:48:59.350014Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x280.8 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "monoforest.plot_features_strength(model, height_per_feature=0.3, width_per_plot=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead of using these handy functions you can get explanation for each feature and analyze it by your custom methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-13T14:49:02.405591Z",
     "start_time": "2019-11-13T14:49:02.391943Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Feature:  1\n",
      "Bias:  [22.377878094259746]\n",
      "Value changes:\n",
      "(border=6.25, probability=0.2648221343873518, value_change=[0.013055730511898902])\n",
      "(border=20.5, probability=0.19960474308300397, value_change=[-0.01966157944026211])\n",
      "(border=21.5, probability=0.191699604743083, value_change=[0.0006295725366007092])\n",
      "(border=26.5, probability=0.15217391304347827, value_change=[0.03658268637094144])\n",
      "(border=29.0, probability=0.14624505928853754, value_change=[0.009554202355206024])\n",
      "(border=31.5, probability=0.13438735177865613, value_change=[-0.02494660710687119])\n",
      "(border=42.5, probability=0.1007905138339921, value_change=[-0.018414643084601917])\n",
      "(border=53.75, probability=0.08300395256916997, value_change=[-0.017299300739722454])\n",
      "(border=83.75, probability=0.023715415019762844, value_change=[-0.032556489114970326])\n",
      "(border=87.5, probability=0.019762845849802372, value_change=[0.04547533558079825])\n",
      "(border=92.5, probability=0.009881422924901186, value_change=[-0.032465184490010575])\n"
     ]
    }
   ],
   "source": [
    "explanations = monoforest.explain_features(model)\n",
    "expl = explanations[1]\n",
    "print(\"Feature: \", expl.feature)\n",
    "print(\"Bias: \", expl.expected_bias)\n",
    "print(\"Value changes:\")\n",
    "for border_expl in expl.borders_explanations:\n",
    "    print(border_expl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-13T14:49:02.737493Z",
     "start_time": "2019-11-13T14:49:02.731275Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Feature #0 'CRIM', strength=[-0.2691852093125575]\n",
      "Feature #1 'ZN', strength=[-0.00022083482538737286]\n",
      "Feature #2 'INDUS', strength=[-0.44376248207255986]\n",
      "Feature #3 'CHAS', strength=[0.016342705307803528]\n",
      "Feature #4 'NOX', strength=[-0.43901005024547507]\n",
      "Feature #5 'RM', strength=[1.5275578548079145]\n",
      "Feature #6 'AGE', strength=[-0.2619165200741341]\n",
      "Feature #7 'DIS', strength=[-0.07460416822418729]\n",
      "Feature #8 'RAD', strength=[-0.06745291497828856]\n",
      "Feature #9 'TAX', strength=[-0.3902675270624572]\n",
      "Feature #10 'PTRATIO', strength=[-0.7024190993225915]\n",
      "Feature #11 'B', strength=[0.20847656894632202]\n",
      "Feature #12 'LSTAT', strength=[-4.969616877155354]\n"
     ]
    }
   ],
   "source": [
    "for feature_name, feature_expl in zip(boston.feature_names, explanations):\n",
    "    print(\"Feature #{} '{}', strength={}\".format(feature_expl.feature, feature_name, feature_expl.calc_strength()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example with MNIST dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's take MNIST dataset and find the most important pixels for each digit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-14T06:57:54.764842Z",
     "start_time": "2019-11-14T06:57:24.943494Z"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import fetch_openml\n",
    "mnist = fetch_openml('mnist_784')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-13T14:49:19.599697Z",
     "start_time": "2019-11-13T14:49:15.519343Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 788)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('./mnist.tsv', header=None, sep='\\t')\n",
    "df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-14T07:01:56.518997Z",
     "start_time": "2019-11-14T07:01:56.509773Z"
    }
   },
   "outputs": [],
   "source": [
    "X = mnist.data\n",
    "y = mnist.target.astype(int)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Function $plot\\_features\\_strength$ is not practical here, so we will make custom plots. These images show which areas of image are most important for each digit. For some digits we can distinctly see familiar images. Fitting takes quite a lot of time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-14T07:22:50.831438Z",
     "start_time": "2019-11-14T07:04:33.254820Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting model for digit 0\n",
      "0:\tlearn: 0.6886337\ttotal: 54.6ms\tremaining: 1m 49s\n",
      "200:\tlearn: 0.2700602\ttotal: 10.5s\tremaining: 1m 33s\n",
      "400:\tlearn: 0.1645564\ttotal: 20.8s\tremaining: 1m 23s\n",
      "600:\tlearn: 0.1200061\ttotal: 31.3s\tremaining: 1m 12s\n",
      "800:\tlearn: 0.0953179\ttotal: 41.7s\tremaining: 1m 2s\n",
      "1000:\tlearn: 0.0800424\ttotal: 52.2s\tremaining: 52.1s\n",
      "1200:\tlearn: 0.0695342\ttotal: 1m 2s\tremaining: 41.7s\n",
      "1400:\tlearn: 0.0618217\ttotal: 1m 13s\tremaining: 31.3s\n",
      "1600:\tlearn: 0.0560027\ttotal: 1m 23s\tremaining: 20.8s\n",
      "1800:\tlearn: 0.0513557\ttotal: 1m 33s\tremaining: 10.4s\n",
      "1999:\tlearn: 0.0475162\ttotal: 1m 44s\tremaining: 0us\n",
      "Fitting model for digit 1\n",
      "0:\tlearn: 0.6886548\ttotal: 55.1ms\tremaining: 1m 50s\n",
      "200:\tlearn: 0.2719173\ttotal: 10.7s\tremaining: 1m 36s\n",
      "400:\tlearn: 0.1662741\ttotal: 21.4s\tremaining: 1m 25s\n",
      "600:\tlearn: 0.1212860\ttotal: 32.1s\tremaining: 1m 14s\n",
      "800:\tlearn: 0.0964201\ttotal: 42.8s\tremaining: 1m 4s\n",
      "1000:\tlearn: 0.0804385\ttotal: 53.6s\tremaining: 53.5s\n",
      "1200:\tlearn: 0.0696504\ttotal: 1m 5s\tremaining: 43.5s\n",
      "1400:\tlearn: 0.0619268\ttotal: 1m 17s\tremaining: 32.9s\n",
      "1600:\tlearn: 0.0559649\ttotal: 1m 28s\tremaining: 21.9s\n",
      "1800:\tlearn: 0.0511846\ttotal: 1m 38s\tremaining: 10.9s\n",
      "1999:\tlearn: 0.0473752\ttotal: 1m 49s\tremaining: 0us\n",
      "Fitting model for digit 2\n",
      "0:\tlearn: 0.6890640\ttotal: 57.5ms\tremaining: 1m 54s\n",
      "200:\tlearn: 0.2994832\ttotal: 11.3s\tremaining: 1m 41s\n",
      "400:\tlearn: 0.1962043\ttotal: 22.7s\tremaining: 1m 30s\n",
      "600:\tlearn: 0.1506509\ttotal: 33.9s\tremaining: 1m 18s\n",
      "800:\tlearn: 0.1246201\ttotal: 45.4s\tremaining: 1m 7s\n",
      "1000:\tlearn: 0.1080779\ttotal: 56.9s\tremaining: 56.7s\n",
      "1200:\tlearn: 0.0966143\ttotal: 1m 8s\tremaining: 45.3s\n",
      "1400:\tlearn: 0.0880387\ttotal: 1m 19s\tremaining: 34s\n",
      "1600:\tlearn: 0.0813937\ttotal: 1m 30s\tremaining: 22.6s\n",
      "1800:\tlearn: 0.0759341\ttotal: 1m 42s\tremaining: 11.3s\n",
      "1999:\tlearn: 0.0714204\ttotal: 1m 53s\tremaining: 0us\n",
      "Fitting model for digit 3\n",
      "0:\tlearn: 0.6890833\ttotal: 48ms\tremaining: 1m 35s\n",
      "200:\tlearn: 0.3096050\ttotal: 10.9s\tremaining: 1m 37s\n",
      "400:\tlearn: 0.2101593\ttotal: 21.6s\tremaining: 1m 26s\n",
      "600:\tlearn: 0.1667571\ttotal: 32s\tremaining: 1m 14s\n",
      "800:\tlearn: 0.1415636\ttotal: 42.6s\tremaining: 1m 3s\n",
      "1000:\tlearn: 0.1253437\ttotal: 53.1s\tremaining: 53s\n",
      "1200:\tlearn: 0.1139357\ttotal: 1m 3s\tremaining: 42.3s\n",
      "1400:\tlearn: 0.1052693\ttotal: 1m 14s\tremaining: 31.7s\n",
      "1600:\tlearn: 0.0982453\ttotal: 1m 24s\tremaining: 21.1s\n",
      "1800:\tlearn: 0.0924642\ttotal: 1m 35s\tremaining: 10.5s\n",
      "1999:\tlearn: 0.0876221\ttotal: 1m 45s\tremaining: 0us\n",
      "Fitting model for digit 4\n",
      "0:\tlearn: 0.6889856\ttotal: 59.2ms\tremaining: 1m 58s\n",
      "200:\tlearn: 0.3003855\ttotal: 11.7s\tremaining: 1m 44s\n",
      "400:\tlearn: 0.1995137\ttotal: 23.2s\tremaining: 1m 32s\n",
      "600:\tlearn: 0.1546393\ttotal: 34.7s\tremaining: 1m 20s\n",
      "800:\tlearn: 0.1286827\ttotal: 46.1s\tremaining: 1m 9s\n",
      "1000:\tlearn: 0.1114483\ttotal: 57.8s\tremaining: 57.7s\n",
      "1200:\tlearn: 0.0994419\ttotal: 1m 9s\tremaining: 46.2s\n",
      "1400:\tlearn: 0.0903500\ttotal: 1m 20s\tremaining: 34.6s\n",
      "1600:\tlearn: 0.0829255\ttotal: 1m 32s\tremaining: 23s\n",
      "1800:\tlearn: 0.0768904\ttotal: 1m 43s\tremaining: 11.5s\n",
      "1999:\tlearn: 0.0720119\ttotal: 1m 55s\tremaining: 0us\n",
      "Fitting model for digit 5\n",
      "0:\tlearn: 0.6890813\ttotal: 54.4ms\tremaining: 1m 48s\n",
      "200:\tlearn: 0.3092825\ttotal: 10.3s\tremaining: 1m 32s\n",
      "400:\tlearn: 0.2060985\ttotal: 20.8s\tremaining: 1m 23s\n",
      "600:\tlearn: 0.1592583\ttotal: 31.2s\tremaining: 1m 12s\n",
      "800:\tlearn: 0.1316508\ttotal: 41.6s\tremaining: 1m 2s\n",
      "1000:\tlearn: 0.1133476\ttotal: 52.5s\tremaining: 52.4s\n",
      "1200:\tlearn: 0.1005772\ttotal: 1m 3s\tremaining: 42s\n",
      "1400:\tlearn: 0.0909892\ttotal: 1m 13s\tremaining: 31.6s\n",
      "1600:\tlearn: 0.0834203\ttotal: 1m 24s\tremaining: 21s\n",
      "1800:\tlearn: 0.0772648\ttotal: 1m 34s\tremaining: 10.5s\n",
      "1999:\tlearn: 0.0723895\ttotal: 1m 45s\tremaining: 0us\n",
      "Fitting model for digit 6\n",
      "0:\tlearn: 0.6887300\ttotal: 51.5ms\tremaining: 1m 43s\n",
      "200:\tlearn: 0.2784226\ttotal: 10.2s\tremaining: 1m 31s\n",
      "400:\tlearn: 0.1744629\ttotal: 20.5s\tremaining: 1m 21s\n",
      "600:\tlearn: 0.1298869\ttotal: 30.8s\tremaining: 1m 11s\n",
      "800:\tlearn: 0.1048753\ttotal: 41.1s\tremaining: 1m 1s\n",
      "1000:\tlearn: 0.0892252\ttotal: 51.3s\tremaining: 51.2s\n",
      "1200:\tlearn: 0.0783053\ttotal: 1m 1s\tremaining: 41.1s\n",
      "1400:\tlearn: 0.0701955\ttotal: 1m 12s\tremaining: 31.1s\n",
      "1600:\tlearn: 0.0639808\ttotal: 1m 23s\tremaining: 20.8s\n",
      "1800:\tlearn: 0.0590000\ttotal: 1m 33s\tremaining: 10.4s\n",
      "1999:\tlearn: 0.0550403\ttotal: 1m 44s\tremaining: 0us\n",
      "Fitting model for digit 7\n",
      "0:\tlearn: 0.6889003\ttotal: 52.6ms\tremaining: 1m 45s\n",
      "200:\tlearn: 0.2882305\ttotal: 10.3s\tremaining: 1m 32s\n",
      "400:\tlearn: 0.1863160\ttotal: 20.8s\tremaining: 1m 22s\n",
      "600:\tlearn: 0.1424369\ttotal: 31.2s\tremaining: 1m 12s\n",
      "800:\tlearn: 0.1176086\ttotal: 41.9s\tremaining: 1m 2s\n",
      "1000:\tlearn: 0.1018302\ttotal: 52.7s\tremaining: 52.6s\n",
      "1400:\tlearn: 0.0828708\ttotal: 1m 13s\tremaining: 31.6s\n",
      "1600:\tlearn: 0.0765905\ttotal: 1m 24s\tremaining: 21.1s\n",
      "1800:\tlearn: 0.0714494\ttotal: 1m 35s\tremaining: 10.5s\n",
      "1999:\tlearn: 0.0673038\ttotal: 1m 45s\tremaining: 0us\n",
      "Fitting model for digit 8\n",
      "0:\tlearn: 0.6891252\ttotal: 54.9ms\tremaining: 1m 49s\n",
      "200:\tlearn: 0.3132675\ttotal: 10.8s\tremaining: 1m 36s\n",
      "400:\tlearn: 0.2137957\ttotal: 21.5s\tremaining: 1m 25s\n",
      "600:\tlearn: 0.1696626\ttotal: 32.3s\tremaining: 1m 15s\n",
      "800:\tlearn: 0.1441196\ttotal: 43s\tremaining: 1m 4s\n",
      "1000:\tlearn: 0.1265248\ttotal: 53.7s\tremaining: 53.6s\n",
      "1200:\tlearn: 0.1137200\ttotal: 1m 4s\tremaining: 42.9s\n",
      "1400:\tlearn: 0.1040918\ttotal: 1m 15s\tremaining: 32.2s\n",
      "1600:\tlearn: 0.0965266\ttotal: 1m 25s\tremaining: 21.4s\n",
      "1800:\tlearn: 0.0903674\ttotal: 1m 36s\tremaining: 10.7s\n",
      "1999:\tlearn: 0.0850751\ttotal: 1m 46s\tremaining: 0us\n",
      "Fitting model for digit 9\n",
      "0:\tlearn: 0.6891745\ttotal: 51.9ms\tremaining: 1m 43s\n",
      "200:\tlearn: 0.3166278\ttotal: 11.3s\tremaining: 1m 41s\n",
      "400:\tlearn: 0.2179615\ttotal: 22.8s\tremaining: 1m 30s\n",
      "600:\tlearn: 0.1744296\ttotal: 34.2s\tremaining: 1m 19s\n",
      "800:\tlearn: 0.1488002\ttotal: 45.5s\tremaining: 1m 8s\n",
      "1000:\tlearn: 0.1320419\ttotal: 56.7s\tremaining: 56.6s\n",
      "1200:\tlearn: 0.1204243\ttotal: 1m 8s\tremaining: 45.3s\n",
      "1400:\tlearn: 0.1116435\ttotal: 1m 19s\tremaining: 33.9s\n",
      "1600:\tlearn: 0.1047797\ttotal: 1m 30s\tremaining: 22.6s\n",
      "1800:\tlearn: 0.0991076\ttotal: 1m 41s\tremaining: 11.3s\n",
      "1999:\tlearn: 0.0944193\ttotal: 1m 53s\tremaining: 0us\n"
     ]
    }
   ],
   "source": [
    "fstr_images = []\n",
    "for digit in range(10):\n",
    "    print(\"Fitting model for digit {}\".format(digit))\n",
    "    model = CatBoostClassifier(loss_function='Logloss', iterations=2000, learning_rate=0.02, \n",
    "                               leaf_estimation_iterations=1, leaf_estimation_method=\"Gradient\")\n",
    "    y_digit = (y == digit).astype(int)\n",
    "    model.fit(X, y_digit, verbose=200)\n",
    "    explanations = monoforest.explain_features(model)\n",
    "    fstr = np.zeros(784)\n",
    "    for i in range(784):\n",
    "        fstr[i] = explanations[i].calc_strength(dim=0)\n",
    "    fstr = np.reshape(fstr, (28, 28))\n",
    "    fstr_images.append(fstr)\n",
    "fstr_images = np.array(fstr_images)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-14T07:30:47.353610Z",
     "start_time": "2019-11-14T07:30:45.411140Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1440x720 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(2, 5)\n",
    "fig.set_size_inches(20, 10)\n",
    "for digit in range(10):\n",
    "    ax[digit // 5][digit % 5].imshow(1.0 / (1.0 + np.exp(-200*fstr_images[digit])), cmap='gray')\n",
    "    ax[digit // 5][digit % 5].set_title(\"Digit {}\".format(digit))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
